Interaction-transformation symbolic regression with extreme learning machine

Abstract

Symbolic Regression searches for a mathematical expression that fits the input data set by minimizing the approximation error. The search space explored by this technique is composed of any mathematical function representable as an expression tree. This provides more flexibility for fitting the data but it also makes the task more challenging. The search space induced by this representation becomes filled with redundancy and ruggedness, sometimes requiring a higher computational budget in order to achieve good results. Recently, a new representation for Symbolic Regression was proposed, called Interaction-Transformation, which can represent function forms as a composition of interactions between predictors and the application of a single transformation function. In this work, we show how this representation can be modeled as a multi-layer neural network with the weights adjusted following the Extreme Learning Machine procedure. The results show that this approach is capable of finding equally good or better results than the current state-of-the-art with a smaller computational cost.